1. Technical Field
The present invention relates to a resonator element, a resonator, oscillator, an electronic device, and a moving object.
2. Related Art
A resonator using quartz crystal has been known from the related art (for example, see JP-A-2007-60729 and JP-A-2011-19159). Such a resonator element has excellent frequency-temperature characteristics, and therefore is widely used as a reference frequency source or a transmission source of various electronic devices.
A resonator element of a resonator disclosed in JP-A-2007-60729 is a tuning fork type and includes a base portion and a pair of vibrating arms which extend from the base portion. A pair of grooves are formed on an upper surface and a lower surface of each vibrating arm. A length of each groove is set so as to be 20% to 68% with respect to the entire length of the resonator element. With such a configuration, equivalent series resistance R1 of the resonator element which vibrates in a fundamental mode may be set to be smaller than equivalent series resistance R2 in a second harmonic mode.
However, by setting the length of the groove in the range described above, an electric-field area for exciting the fundamental mode is reduced by an amount of a decreased proportion of the length of the groove with respect to the length of the resonator element, and as a result, the equivalent series resistance R1 is increased.
A resonator element of a resonator disclosed in JP-A-2011-19159 is also a tuning fork type and includes a base portion and a pair of vibrating arms which extend from the base portion. Each vibrating arm includes an arm portion on which a pair of grooves opened to an upper surface and a lower surface thereof are formed, and a hammerhead (weight portion) provided on the arm portion on a side opposite the base portion. A width of the hammerhead is set to be equal to or more than double the width of the arm portion and a length of the hammerhead is set to be equal to or greater than 30% of the length of the vibrating arm, and accordingly vibration in the second harmonic mode which is an unnecessary wave mode may be suppressed.
However, since a proportion of the hammerhead in the resonator element is set to be great, R1 increases as a Q value of the resonator element decreases, in a range of the length of the hammerhead which exceeds 41% of the length of the vibrating arm. Even in a range of the length of the hammerhead which is 30% to 41% of the length of the vibrating arm, the length of the arm portion on which the groove is formed is small and the electric-field area for exciting the fundamental mode is small, and accordingly an electric-field effect is decreased and the equivalent series resistance R1 increases.
As described above, in the resonator element of the related art, it was difficult to suppress the increase of the equivalent series resistance R1 and to set the equivalent series resistance R1 to be smaller than the equivalent series resistance R2 in the unnecessary wave mode. That is, in the resonator element of the related art, it was difficult to satisfy both the reduction of a concern of a false operation in which an oscillator with the resonator element loaded thereon oscillates at a resonance frequency in the unnecessary wave mode, and the decrease of the equivalent series resistance R1.